Temperature dependence of the band gap of silicon

Abstract

The band‐gap energy E_g of silicon has been reevaluated with high precision between 2 and 300 K by the following method: the derivative of the absorption coefficient, resulting from free‐exciton absorption, has a well‐defined singularity, which can be detected unambiguously by wavelength‐modulation spectroscopy. The energy of this singularity yields the band gap. Our data deviated by more than 5 meV from the earlier results of MacFarlane et al. and Haynes et al. and fell between their E_g(T) curves. The approximation of E_g(T) = A + BT + CT² gives A = 1.170 eV, B = 1.059×10⁻⁵ eV/K, and C = −6.05×10⁻⁷ eV/K², for 0<T≤190 K, and A = 1.1785 eV, B = −9.025×10⁻⁵ eV/K, and C = −3.05×10⁻⁷ eV/K², for 150≤T≤300 K, which fits our data within 0.2 meV. The major uncertainty of about 1 meV lies in the energies of exciton and TO phonon.